1. Let T:VV be a linear operator, where V is an n-dimensional vector space over F. Also let and be two arbitrary ordered bases for V. Prove that det([T]tIn)=det([T]tIn) 2. Let T be a linear operator on a finite-dimensional vector space V, and let be an ordered basis for V. (1) Prove that is an eigenvalue of T if and only if is an eigenvalue of [T]. (2) Prove that v is an eigenvector of T corresponding to if and only if [v] is an eigenvector of [T] corresponding to